Speaking in the House of Commons on Tuesday, Mr Brokenshire said the "clock was ticking" and that if there was no resolution between Sinn Fein and the Democratic Unionists, there would be an election within seven days.

He warned that an election would "deepen divisions" in Northern Ireland.

Mr Brokenshire said: "The situation we face in Northern Ireland today is grave and the Government treats it with the utmost seriousness."

He added: "We do, however, have to be realistic. The clock is ticking.

Video:McGuinness: DUP is in 'fool's paradise'

"If there is no resolution then an election is inevitable despite the widely held view that this election may deepen divisions and threaten the continuation of the devolved institutions."

Mr McGuinness resigned over the Renewable Heat Incentive (RHI), known as "cash for ash", overseen by First Minister Arlene Foster when she was enterprise minister, and which could cost taxpayers £400m.

The state-funded environmental scheme was supposed to offer businesses a proportion of the cost of running eco-friendly boilers.

But the subsidy tariffs were set too high and, without a cap, resulting in Stormont paying out significantly more than the price of fuel.

Video:Arlene Foster: Sinn Fein's action 'selfish'

Mrs Foster said on Tuesday that the investigation into the scheme, and her part in it, could now go ahead given that she was no longer First Minister but that she was confident she did nothing wrong.

Mr McGuinness had demanded that Mrs Foster step down while the investigation took place but she refused, sparking his resignation.

Sinn Fein has signalled it will not replace Mr McGuinness and he warned in his resignation statement that there would be no return to the "status quo".